Method of testing hardness of micro region

ABSTRACT

A testing method is provided for determining the hardness of a micro region, using indentation curves indicating relations between observed penetration depths and indenting forces when an arbitrary shaped indenter is pushed into standard samples of plural types. The method involves (1) measuring relations between observed penetration depths and indenting forces when the arbitrary shaped indenter is pushed into standard samples of plural types, to prepare the indentation curves, (2) determining a reference function indicative of macro hardness, by standardizing the relations between the indenting forces and macro hardness at the same penetration depth as an index, for the indentation curves of the standard samples of plural types, (3) measuring a relation between the penetration depth and indenting force of an arbitrary sample, and (4) determining the hardness of a micro region from the measured value in step (3) according to the reference function as determined in step (2).

This application is a 371 of PCT/JP99/01565 filed Mar. 26, 1999.

TECHNICAL FIELD

This invention concerns a method of testing hardness of a micro region.More specifically, it relates to a novel method of testing hardnesscapable of accurately evaluating the hardness of a micro region such asa nanometer region that can not be measured by a test for macro hardnesssuch as Vickers hardness.

BACKGROUND ART

Heretofore, in a Vickers hardness test which is typical for the macrohardness test, the hardness has been determined in accordance with adefinition of dividing an indenting force with an area of contact. Sincethere is no substantial size effect in the macro hardness, the indentingforce with force employed is usually properly selected.

On the contrary, in the hardness test for a micro region such as ananometer region, when the hardness is calculated in accordance with thedefinition based on a measured indenting force and a penetration depthas usual, it results in a problem that an apparent hardness increasessince the size effect is not negligible. Then, it is necessary toeliminate the influence of the size effect. In the existent method, acorrelation is determined between a hardness determined at a certainpenetration depth in accordance with the definition and a macrohardness, or an indentation curve is approximated by a certain functionand a correlation between the parameter and the hardness is determined.

However, the existent study for the correlation with the macro hardnessis scarcely considered effective. For an arbitrary sample, the hardnessof a micro region can not accurately be evaluated at present.

On the other hand, evaluation for the hardness of the micro region hasprovided an extremely important subject for the research and developmentof new metal materials and semiconductors.

In view of the above, it is a subject of the invention in theapplication to overcome the limit of the prior art as described above inindenting an indenter into a sample and evaluating the hardness of amaterial based on a relation between an indenting force and apenetration depth, and provide a novel method eliminating the influenceof the size effect that the apparent hardness increases in the test forthe hardness of a micro region with the penetration depth or an indentdepth of 1 μm or less, considering the micro hardness in the microhardness test in the same manner as in the macro hardness in the Vickershardness test, and capable of effectively utilizing the existentknowledge for the macro hardness and accurately evaluating the hardnessof a nanometer region.

SUBJECT OF THE INVENTION

The invention of the application, for solving the foregoing subject,provides a testing method for determining the hardness of a microregion, into which an indenter is pushed, from an indentation curveindicating a relation between a penetration depth observed when anindenter in an arbitrary shape is pushed in and an indenting force,characterized by comprising

(1) measuring, in addition to macro hardnesses, relations betweenpenetration depths observed when an indenter in an arbitrary shape ispushed in and indenting forces, for a plurality types of standardsamples,

(2) determining a reference function indicating a macro hardness bystandardizing a relation between an indenting force and a macro hardnesswith the same penetration depth used as an index, for indentation curvesof a plurality types of standard samples indicating relations betweenpenetration depths and indenting forces,

(3) measuring relations between penetration depths and indenting forcesfor arbitrary samples, and

(4) determining the hardness of a micro region from the measured valuesaccording to the reference function.

Further, according to the invention of this application, a plurality ofstandard samples having identical mechanical properties in themicrometer region and the nanometer region are used in the methoddescribed above.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph illustrating indentation curves on electrolyticallypolished surfaces for each of metal single crystals (60° indenter),

FIG. 2 is a graph illustrating indentation curves on theelectrolytically polished surfaces for each of metal single crystals(115° indenter),

FIG. 3 is a graph illustrating relations between indenting forces andVickers hardness (60° indenter),

FIG. 4 is a graph illustrating relations between indenting forces andVickers hardness (115° indenter),

FIG. 5 is a graph illustrating a relation between a standardizedindenting force and a penetration depth (60° indenter).

FIG. 6 is a graph illustrating a relation between a standardizedindenting force and a penetration depth (115° indenter).

FIG. 7 is a graph illustrating indentation curves for buff polishedsurfaces and electrolytically polished surfaces for nickel and tungsten(60° indenter),

FIG. 8 is a graph illustrating relation between the hardness of nickeland penetration depth,

FIG. 9 is a graph illustrating relation between the hardness of tungstenand penetration depth,

FIG. 10 is a graph illustrating an indentation curve for ferritic steel(60° indenter),

FIG. 11 is a graph illustrating a hardness of ferritic steel,

FIG. 12 is an AFM image diagram obtained after conducting an indentingtest on inclusions,

FIG. 13 is a graph showing indentation curves for inclusions (60°indenter),

FIG. 14 is a graph illustrating the hardness of inclusions,

FIG. 15 is schematic views in the hardness test for a composite phasesamples and a single phase samples,

FIG. 16 is a comparative graph between the hardness by a Vickershardness test and the hardness by an ultra-micro hardness test.

BEST MODE FOR PRACTICING THE INVENTION

The invention of the application has the features as described above andembodiments will be explained.

In this invention, the correlation with the result of a macro hardnesstest such as by a Vickers test or a Knoop test is considered with a newpoint of view. Then, for the hardness test of a micro region, indentersof arbitrary shape are used, and a relation between the penetrationdepth and the indenting force by the indenter is noted in thisinvention.

For indentation of the indenter, a cantilever system or double leversystem and various other types of systems, as well as apparatus thereformay be used.

Then, examples are shown below and the test method according to thisinvention is to be explained with reference to the examples.

EXAMPLE

At first, in the method of this invention, as a first step of a testmethod for determining the hardness of a micro region into which anindenter is pushed, from an indentation curve indicating a relationbetween a penetration depth observed when an indenter in an arbitraryshape is pushed in and an indenting force,

(1) relations between penetration depths observed when an indenter in anarbitrary shape is pushed in and indenting forces are measured for aplurality types of standard samples as described above.

The standard samples may be in any combination of a plurality of speciessuch as iron, nickel and molybdenum. However, it is appropriate thateach of the standard samples has an identical mechanical properties inthe macro meter region and the nanometer region.

Further, for the standard samples, single structure materials orcomposite phase fine structure materials are selected. It is notpreferred that the materials have a layer different in the mechanicalproperties such as a surface treated layer.

In the examples, single crystals of tungsten, molybdenum, nickel andiron were used as the single phase material for the standard samples.

For removing the surface treated layer, the surfaces of the samples wereelectrolytically polished. A micro Vickers test and a micro hardnesstest by indentation of indenters were conducted for each of the samples.Data from the micro hardness test were obtained by a micro hardness testmethod based on an inter-atomic force microscope (AFM). For theindenters, two types of diamond triangular pyramidal indenters with anapex of 60° and 115° were used.

FIG. 1 and FIG. 2 are indentation curves indicating relations betweenpenetration depth (nm) by a 60° indenter and a 115° indenterrespectively and indenting forces: F(μN) for each of the standardsamples.

Then as described above, in this invention, as the next step:

(2) a reference function indicating a macro hardness is determined bystandardizing a relation between an indenting force and a macro hardnesswith the same penetration depth used as an index is determined forindentation curves of a plurality types of standard samples indicatingrelations between penetration depths and indenting forces.

That is, specifically, when a relation between the indenting force F(μN) and the Vickers hardness HV required for giving a certainpenetration depth h (nm) is determined at first from the indentationcurves shown in FIG. 1 and FIG. 2, results in FIG. 3 and FIG. 4 areobtained. The relation between the indenting force: F and the Vickershardness: HV gives straight lines each of an identical gradient in aboth logarithmic graph at a penetration depth of 100 nm or more for the60° indenter in FIG. 3 and at a penetration depth of 500 nm or more forthe 115° indenter in FIG. 4. They are represented by the followingequations.

HV=a·F ^(n)  (1)

n=1.214(60° indenter)  (2)

n=1.023(115° indenter)  (3)

in which a represents a coefficient.

The foregoing indicate that indentation curves for different samples canbe standardized as F/HV^((t/n)).

FIG. 5 and FIG. 6 show the relations between F/HV^((t/n)) and thepenetration depth: h. As a result of trying various functions, goodapproximation can be obtained by the following functions for the case ofthe 60° indenter and 115° indenter respectively in the examples.

F/HV ^((t/n))=5.6634×10⁻⁵(h+122.83)² . . . 60° indenter  (4)

F/HV ^((t/n))=4.6248×10⁻⁴(h+40.468)² . . . 115° indenter  (5)

When rewritten, the Vickers hardness: HV is finally represented as arelation between the penetration depth: h (nm) and the indenting force:F (μN) by the following reference functions.

F/HV ^((t/n)) =[F/{5.6634×10⁻⁵(h+122.83)²}]^(1.214) . . . 60°indenter  (6)

F/HV ^((t/n)) =[F/{4.6248×10⁻⁴(h+40.468)²}]^(1.023) . . . 115°indenter  (7)

Then, as the final step, in this invention,

(3) the relations between the penetration depth and the indenting forceare measured for arbitrary samples and

(4) the hardness of a micro region is determined from the measuredvalues according to the reference function.

For instance, the hardness is determined also as the evaluation for theinfluence of the surface layer as below.

That is, for examining the influence of the surface layer, a ultra-microhardness test on the polished surface of nickel and tungsten singlecrystals was conducted by using a 60° indenter. FIG. 7 shows indentationcurves. Then, the hardness was determined by applying the referencefunction of the equation (6) to the result of FIG. 7. As a result inaccordance with the reference function, FIG. 8 shows the Vickershardness: HV in the case of nickel and FIG. 9 shows the Vickershardness: HV in the case of tungsten. For the reference, a hardness: Humdetermined by dividing the indentation force with an area of contact inaccordance with the ordinary definition is also shown. While thehardness Hum in accordance with the existent definition shows a sizeeffect that the hardness value increases as the penetration depthdecreases, such influence of the size effect does not appear in thehardness calculated in accordance with the reference function of theequation (6). The hardness of the buff polished surface is greater thanthat on the electrolytically polished surface, which is considered to bethe effect of the surface treated layer. In view of the above, it can besaid that the buff polished surface having not uniform mechanicalproperties relative to the direction of the depth is not appropriate asthe standard sample.

Further, FIG. 10 is an indentation curve for ferritic steels obtained byusing the same 60° indenter. FIG. 11 shows the hardness: HV calculatedby using the reference function of the equation (6) from FIG. 10. Thehardness in the region free from the influence of the size effect isabout 110 to 120, which shows a value approximate to hardness 111 by theVickers hardness to make it clear that the method of this invention ispractically useful. Hardness in both of the cases is identical in thiscase because the crystal grain size of the ferritic steel is as large asabout 50 μm and the crystal grain boundary gives no substantial effecton the macro hardness. Naturally, since the micro harness is measured inthe grains, it is quite free from the effect of the grain boundary.

As a further test, a ultra-micro hardness test for inclusions containedin the steels was conducted. FIG. 12 shows an AFM image after the testof SiO₂ type inclusions. The composition of the inclusions is previouslyanalyzed by EDX. Indentation curves for each of SiO₂ type and MnS typeinclusions are as shown in FIG. 13 respectively. When the hardness iscalculated from respective penetration depths in accordance with thereference function of the equation (6), they are as shown in FIG. 14, inwhich the hardness is 100 for MnS and the hardness is 430 for SiO₂. Asdescribed above, it has been found according to this invention that thehardness of inclusions with a diameter of several μm can be evaluated.

Referring further to the standard samples, composite phase materialssuch as iron and steel materials have often been used as standardsamples for the existent macro hardness test. In a case where thehardness in the macro test is related with the indentation curve in theultra-macro region in this invention, it is preconditions that thematerial has identical mechanical properties in both of the tests. FIG.15 is schematic views in a case of testing the composite phase materialby a macro hardness test and a ultra-micro hardness test. The compositephase material is reinforced with crystal grain boundary or precipitatesand, when the distance of dispersion between them is several μm or more,their effects appear in the macro test but do not appear in theultra-macro hardness test. Accordingly, they are not appropriate as thestandard sample. On the contrary, since it is considered that thecharacteristics of the single structure material are identicalirrespective of the size of the tested region, this appropriate as thestandard sample. Also in the case of the composite phase material, sinceit is considered that the mechanical properties are identical betweenthe macro hardness test and the ultra-micro hardness test for the finecomposite phase material in which the distance of dispersion in thestrengthening mechanism is at a nanometer order, this material isappropriate as the standard sample. FIG. 16 shows a relation between thehardness obtained by a Vickers test and the hardness obtained bysubstituting the reference function of the equation (6) according tothis invention for the indenting force of 445 μN. With respect to thestandard curve for the single crystals as the single material, practicalsteels have increased hardness by the Vickers test with the reasons asdescribed above. It is clearly shown that the single material such assingle crystals is preferred as the standard sample.

INDUSTRIAL APPLICABILITY

According to the invention of this application, as has been explainedspecifically above, the hardness of the micro region can be evaluatedaccurately.

In the study directed to the nanometer region, since observing equipmentsuch as TEM, analyzers such as AES and AP are utilized, the microhardness test of this invention can contribute to the development ofmaterials in cooperation with the apparatus described above as the meansfor evaluating the mechanical properties.

Further, also with a practical point of view, the hardness evaluationmethod is used in various fields and progress in the research anddevelopment can be expected, and it can improve the reliability and theproduction efficiency when utilized as the quality control means inactual production sites.

What is claimed is:
 1. A testing method for determining the hardness ofa micro region. using indentation curves indicating relations betweenobserved penetration depths and indenting forces when an arbitraryshaped indenter is pushed into standard samples of plural types,comprising: (1) measuring relations between observed penetration depthsand indenting forces when the arbitrary shaped indenter is pushed intostandard samples of plural types, to prepare the indentation curves, (2)determining a reference function indicative of macro hardness, bystandardizing the relations between the indenting forces and macrohardness at the same penetration depth as an index, for the indentationcurves of the standard samples of plural types, (3) measuring a relationbetween the penetration depth and indenting force of an arbitrarysample, and (4) determining the hardness of a micro region from themeasured value in step (3) according to the reference function asdetermined in step (2).
 2. The method according to claim 1, wherein eachstandard sample of plural types has an identical mechanical property inthe micrometer region and the nanometer region.
 3. A method fordetermining the hardness of a micro region of a test sample, whichcomprises: providing a plurality of different standard samples,contacting each standard sample with an indenter at a plurality ofdifferent indenting forces, to thereby cause the indenter to penetrateeach standard sample at different penetration depths, measuring thepenetration depth formed in each standard sample under each indentingforce, determining a relationship between the penetrating depths andindenting forces for each standard sample, determining a standardizedrelationship between indenting force and macro hardness for theplurality of different standard samples using the same penetration depthas an index, determining a reference function between indenting force,macro hardness and penetration depth for an arbitrary test sample,contacting the test sample with the indenter at an indenting force, andmeasuring the penetration depth formed in the test sample under theindenting force, determining the hardness of the micro region of thetest sample using the reference function.
 4. The method according toclaim 3, wherein the step of determining the relationship between thepenetrating depths and indenting forces for each standard sampleincludes a step of preparing indentation curves for each standardsample.
 5. The method according to claim 3, wherein the plurality ofdifferent standard samples are selected from iron, nickel, molybdenumand tungsten.
 6. The method according to claim 3, wherein the standardsamples are single crystals.
 7. The method according to claim 3, whereinthe standard samples have electrolytically polished surfaces or buffedpolished surfaces.
 8. The method according to claim 3, wherein theindenter is a diamond pyramidal indenter.
 9. The method according toclaim 3, wherein the indenter has an apex of 60° or 115°.
 10. The methodaccording to claim 3, wherein each different standard sample has anidentical mechanical property in the micrometer region and in thenanometer region.